U.S. patent application number 16/598667 was filed with the patent office on 2020-05-21 for methods, systems and apparatus to improve the efficiency of calculating a customer retention rate.
The applicant listed for this patent is The Nielsen Company (US), LLC. Invention is credited to Ludo Daemen, Michael Sheppard.
Application Number | 20200160357 16/598667 |
Document ID | / |
Family ID | 62243976 |
Filed Date | 2020-05-21 |
![](/patent/app/20200160357/US20200160357A1-20200521-D00000.png)
![](/patent/app/20200160357/US20200160357A1-20200521-D00001.png)
![](/patent/app/20200160357/US20200160357A1-20200521-D00002.png)
![](/patent/app/20200160357/US20200160357A1-20200521-D00003.png)
![](/patent/app/20200160357/US20200160357A1-20200521-D00004.png)
![](/patent/app/20200160357/US20200160357A1-20200521-M00001.png)
![](/patent/app/20200160357/US20200160357A1-20200521-M00002.png)
![](/patent/app/20200160357/US20200160357A1-20200521-M00003.png)
![](/patent/app/20200160357/US20200160357A1-20200521-M00004.png)
![](/patent/app/20200160357/US20200160357A1-20200521-M00005.png)
![](/patent/app/20200160357/US20200160357A1-20200521-M00006.png)
View All Diagrams
United States Patent
Application |
20200160357 |
Kind Code |
A1 |
Sheppard; Michael ; et
al. |
May 21, 2020 |
METHODS, SYSTEMS AND APPARATUS TO IMPROVE THE EFFICIENCY OF
CALCULATING A CUSTOMER RETENTION RATE
Abstract
Methods, systems and apparatus to improve the efficiency of
calculating a customer retention rate are disclosed herein. An
example apparatus described herein that may be implemented to
calculate a customer retention rate includes a retention rate model
generator to generate a baseline retention rate model based on
survivability data associated with an observed duration of
interest, a shifted-beta-geometric distribution generator to
generate a shifted-beta-geometric distribution model based on the
survivability data, a model modifier to modify the baseline
retention rate model based on the shifted-beta-geometric
distribution model to create a modified retention rate model, and a
model comparator to reduce a computational burden of calculating
the customer retention rate by merging the modified retention rate
model with the baseline retention rate model to generate a merged
shifted-beta-geometric model, the merged shifted-beta-geometric
model including first and second shifted-beta-geometric model
parameters to determine the customer retention rate.
Inventors: |
Sheppard; Michael; (Holland,
MI) ; Daemen; Ludo; (Duffel, BE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
The Nielsen Company (US), LLC |
New York |
NY |
US |
|
|
Family ID: |
62243976 |
Appl. No.: |
16/598667 |
Filed: |
October 10, 2019 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
15371658 |
Dec 7, 2016 |
|
|
|
16598667 |
|
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06Q 10/067 20130101;
G06Q 30/0201 20130101 |
International
Class: |
G06Q 30/02 20060101
G06Q030/02; G06Q 10/06 20060101 G06Q010/06 |
Claims
1. An apparatus to determine a customer retention rate, the
apparatus comprising: a retention rate model generator to generate
a baseline retention rate model based on survivability data
associated with an observed duration of interest; a
shifted-beta-geometric distribution generator to generate a
shifted-beta-geometric distribution model based on the
survivability data; a model modifier to modify the baseline
retention rate model based on the shifted-beta-geometric
distribution model to create a modified retention rate model; a
model comparator to reduce a computational burden of calculating
the customer retention rate by merging the modified retention rate
model with the baseline retention rate model to generate a merged
shifted-beta-geometric model, the merged shifted-beta-geometric
model including first and second shifted-beta-geometric model
parameters to determine the customer retention rate; a variable
definer to define a survivability variable of the survivability
data, the survivability variable corresponding to a predicted
customer retention rate based on the merged shifted-beta-geometric
model and a number of active customers; and a linear relationship
definer to facilitate linear least squares solving of the first and
second shifted-beta-geometric model parameters by establishing a
linear relationship therebetween, the customer retention rate
determined based on the first and second shifted-beta-geometric
model parameters, the first and second shifted-beta-geometric model
parameters fitted to the modified retention rate model.
2. The apparatus as defined in claim 1, further including a
customer data storage to store customer data, including the
survivability data.
3. The apparatus as defined in claim 2, further including a
survivability data retriever to retrieve customer survivability
data from the customer data storage.
4. The apparatus as defined in claim 1, further including a
parameter estimator to estimate the shifted-beta-geometric model
parameters based on the merged shifted-beta-geometric model.
5. The apparatus as defined in claim 1, further including a
retention rate estimator to determine the retention rate based on
the shifted-beta-geometric model parameters and the merged
shifted-beta-geometric model.
6. The apparatus as defined in claim 1, wherein the model
comparator further includes: a parameter solver to solve the
shifted-beta-geometric model for one of the shifted-beta-geometric
model parameters; a simplifier to substitute the survivability
variable into the shifted-beta-geometric model to simplify the
shifted-beta-geometric model; a matrix definer to define a matrix
based on the linear relationship between the first and second
shifted-beta-geometric model parameters; and an equation generator
to generate a system of equations based on the matrix to be
implemented to determine the customer retention rate.
7. The apparatus as defined in claim 6, wherein the system of
equations is derived from the matrix.
8. A computer-implemented method to determine a customer retention
rate, the method comprising: generating, by executing an
instruction with a processor, a baseline retention rate model based
on survivability data associated with an observed duration of
interest; generating, by executing an instruction with the
processor, a shifted-beta-geometric distribution model based on the
survivability data; modifying, by executing an instruction with the
processor, the baseline retention rate model based on the
shifted-beta-geometric distribution model to create a modified
retention rate model; reducing a computational burden of
calculating the customer retention rate by merging, by executing an
instruction with the processor, the modified retention rate model
with the baseline retention rate model to generate a merged
shifted-beta-geometric model, the merged shifted-beta-geometric
model including first and second shifted-beta-geometric model
parameters to determine the customer retention rate; defining, by
executing an instruction with the processor, a survivability
variable of the survivability data, the survivability variable
corresponding to a predicted customer retention rate based on the
merged shifted-beta-geometric model and a number of active
customers; and facilitating, by executing an instruction with the
processor, linear least squares solving of the first and second
shifted-beta-geometric model parameters by establishing a linear
relationship therebetween, the customer retention rate determined
based on the first and second shifted-beta-geometric model
parameters, the first and second shifted-beta-geometric model
parameters fitted to the modified retention rate model.
9. The method as defined in claim 8, further including retrieving
customer survivability data from a customer data storage.
10. The method as defined in claim 9, further including estimating
the shifted-beta-geometric model parameters based on the merged
shifted-beta-geometric model.
11. The method as defined in claim 8, further including calculating
the retention rate based on the shifted-beta-geometric model
parameters and the merged shifted-beta-geometric model.
12. The method as defined in claim 8, further including
establishing a linear relationship between a first one of the
shifted-beta-geometric model parameters and a second one of the
shifted-beta-geometric model parameters.
13. The method as defined in claim 12, further including defining a
matrix based on the linear relationship between the first and
second shifted-beta-geometric model parameters.
14. The method as defined in claim 13, further including generating
a system of equations to be implemented to determine the customer
retention rate.
15. A tangible machine readable storage medium comprising
instructions that, when executed, cause a machine to at least:
generate a baseline retention rate model based on survivability
data associated with an observed duration of interest; generate a
shifted-beta-geometric distribution model based on the
survivability data; modify the baseline retention rate model based
on the shifted-beta-geometric distribution model to create a
modified retention rate model; reduce a computational burden of
calculating a customer retention rate by merging the modified
retention rate model with the baseline retention rate model to
generate a merged shifted-beta-geometric model, the merged
shifted-beta-geometric model including first and second
shifted-beta-geometric model parameters to determine the customer
retention rate; define a survivability variable of the
survivability data, the survivability variable corresponding to a
predicted customer retention rate based on the merged
shifted-beta-geometric model and a number of active customers; and
facilitate linear least squares solving of the first and second
shifted-beta-geometric model parameters by establishing a linear
relationship therebetween, the customer retention rate determined
based on the first and second shifted-beta-geometric model
parameters, the first and second shifted-beta-geometric model
parameters fitted to the modified retention rate model.
16. The tangible machine readable storage medium of claim 15,
wherein the instructions, when executed, cause the machine to
retrieve customer survivability data from a customer data
storage.
17. The tangible machine readable storage medium of claim 16,
wherein the instructions, when executed, cause the machine to
estimate the shifted-beta-geometric model parameters based on the
merged shifted-beta-geometric model.
18. The tangible machine readable storage medium of claim 15,
wherein the instructions, when executed, cause the machine to
determine the retention rate based on the shifted-beta-geometric
model parameters and the merged shifted-beta-geometric model.
19. The tangible machine readable storage medium of claim 15,
wherein the instructions, when executed, cause the machine to
generate a system of equations to be implemented to determine the
customer retention rate.
Description
FIELD OF THE DISCLOSURE
[0001] This disclosure relates generally to customer retention and,
more particularly, to methods, systems, and apparatus to improve
the efficiency of calculating a customer retention rate.
BACKGROUND
[0002] In recent years, customer retention has been predicted using
models that estimate unknown retention rate data based on a known
retention rate for a period of time. Modeling customer retention is
helpful to gain valuable insight related to customer behavior and
loyalty. This is particularly true in view of customer behaviors
that are relatively dynamic, such as dynamic churn behaviors of
customers/consumers that join and leave mobile phone providers,
and/or other service contracts.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] FIG. 1 is a schematic illustration of an example customer
retention analysis engine constructed in accordance with the
teachings of this disclosure to calculate a customer retention
rate.
[0004] FIG. 2 is a schematic illustration of an example model
comparator that may be implemented with the example customer
retention analysis to determine a predicted customer retention.
[0005] FIGS. 3-4 are flowcharts representative of example machine
readable instructions that may be executed to implement the example
product analysis engine of FIG. 1 and/or the example comparator of
FIG. 2.
[0006] FIG. 5 is a block diagram of an example processor platform
structured to execute the example machine readable instructions of
FIGS. 3-4 to implement the example product analysis engine of FIG.
1 and/or the example comparator of FIG. 2.
[0007] The figures are not to scale. Instead, to clarify multiple
layers and regions, the thickness of the layers may be enlarged in
the drawings. Wherever possible, the same reference numbers will be
used throughout the drawing(s) and accompanying written description
to refer to the same or like parts.
DETAILED DESCRIPTION
[0008] Modeling and predicting customer retention is an important
aspect of customer behavior and loyalty. Customer retention
represents a number of customers that have remained participants of
a product or service of interest from a first time (e.g., a
starting time, t=0 minutes, hours, weeks, months, years, etc.) to a
second time (e.g., a current time such as five years after the
starting time, t=5 years). Current techniques to model customer
retention rates may use Maximum Likelihood (MLE) procedures to
estimate parameters of a shifted-beta geometric (sBG) distribution
model. In one example, an sBG model is used to model the retention
rate over a period of time in which parameters of the sBG model are
determined using algorithms. In an example technique to determine
the retention rate of customers, a probability that a customer has
survived (e.g., is still active) at a given time is determined. The
retention rate is a proportion of customers still active at the end
of a time period of interest based on a probability that a customer
has survived. Based on the probability, traditional techniques
apply the computationally intensive MLE procedures to determine a
prediction for an expected tenure or lifetime of a customer. The
customer lifetime can be predicted based on available data for a
first time period. Such computationally intensive MLE procedures
invoke many modeling iterations (e.g., hundreds or thousands of
iterations) to determine the customer retention rate. Estimating
the parameters using such complicated computational techniques
requires a large amount of computational memory and performance for
one or more processors.
[0009] In some examples, an sBG probability is implemented to
estimate whether a randomly chosen customer will have a particular
lifetime (e.g., one year, two years, etc.). The traditional sBG
probability techniques include parameters .alpha. and .beta.. To
determine the values of .alpha. and .beta., which are used to
estimate the sBG probability, numerical optimization methods (e.g.,
iterations using a solver) are used. The resulting values for
.alpha. and .beta. are called maximum likelihood estimates of the
sBG parameters .alpha. and .beta.. In some examples, a
log-likelihood function is maximized to determine the maximum
likelihood estimates of the sBG parameters .alpha. and .beta.. To
verify the estimated values of the sBG parameters .alpha. and
.beta., the MLE procedures are repeated using a different set of
starting values. The customer retention rate can then be calculated
using an sBG distribution model. Due to the iterations and
repetition of the traditional MLE procedures, this method of
determining a customer retention rate is computationally intensive
(e.g., for processors of a machine).
[0010] An example apparatus disclosed herein calculates a customer
retention rate with a retention rate model generator to generate a
baseline retention rate model based on survivability data
associated with an observed duration of interest, a
shifted-beta-geometric distribution generator to generate a
shifted-beta-geometric distribution model based on the
survivability data, a model modifier to modify the baseline
retention rate model based on the shifted-beta-geometric
distribution model to create a modified retention rate model, and a
model comparator to reduce a computational burden of calculating
the customer retention rate by merging the modified retention rate
model with the baseline retention rate model to generate a merged
shifted-beta-geometric model, the merged shifted-beta-geometric
model including a shifted-beta-geometric model parameters to
determine the customer retention rate.
[0011] Example apparatus disclosed herein also include a customer
data storage to store customer data, including survivability data.
Example apparatus disclosed herein also include a survivability
data retriever to retrieve customer survivability data from the
customer data storage. Example apparatus disclosed herein also
include a parameter estimator to estimate the
shifted-beta-geometric model parameters based on the merged
shifted-beta-geometric model. Example apparatus disclosed herein
also include a retention rate estimator to calculate the retention
rate based on the shifted-beta-geometric model parameters and the
merged shifted-beta-geometric model. Example model comparators
disclosed herein include a parameter solver to solve the
shifted-beta-geometric model for one of the shifted-beta-geometric
model parameters, a variable definer to define a survivability
variable related to the survivability of a customer based on the
merged shifted-beta-geometric model, a simplifier to substitute the
survivability variable into the shifted-beta-geometric model to
simplify the shifted-beta-geometric model, a linear relationship
definer to establish a linear relationship between a first one of
the shifted-beta-geometric model parameters and a second one of the
shifted-beta-geometric model parameters, a matrix definer to define
a matrix based on the linear relationship between the first and
second shifted-beta-geometric model parameters, and an equation
generator to generate a system of equations to be implemented to
determine the customer retention rate.
[0012] FIG. 1 is a schematic illustration of an example customer
retention analysis engine 100 coupled to an example customer data
storage 102. In the illustrated example of FIG. 1, the customer
retention analysis engine 100 includes a survivability data
retriever 104, a retention rate model generator 106, a shifted
beta-geometric (sBG) distribution generator 108, a model modifier
110, a model comparator 112, a parameter estimator 114, and a
retention rate estimator 116. In operation, the example customer
retention analysis engine 100 estimates a customer retention for a
forecast time period (e.g., a second time period for a future
duration) based on data from a first time period (e.g., a most
recent number of days, months, years, etc.). The example customer
retention analysis engine 100 invokes the survivability data
retriever 104 to obtain and/or otherwise retrieve data from the
customer data storage 102 related to survivability of a customer
(e.g., customer retention) during the first time period. For
example, survivability data may include a number of years each
individual has been a customer of a particular business. In some
examples, the forecast period is set by a user. The forecast period
is a time period for which the user is to predict a retention rate.
For example, a forecast period may be five years.
[0013] The example retention rate model generator 106 generates a
baseline retention rate model based on the survivability data
associated with an observed duration of interest and retrieved by
the survivability data retriever 104. In some examples, the
retention rate model generator 106 generates the baseline retention
rate model in a manner consistent with example Equation 1 to the
acquired survivability data, where r.sub.t is a retention rate, t
is time, and S(t) and S(t-1) are survivor functions indicative of a
survivability (S), which reflects a probability that a customer has
survived to time t or time t-1.
r t = S ( t ) S ( t - 1 ) Equation 1 ##EQU00001##
[0014] The example sBG distribution generator 108 generates a
shifted beta-geometric distribution model of the survivability data
in a manner consistent with example Equation 2. In some examples,
the sBG distribution generator 108 applies example Equation 2 to
apply sBG principles to estimate survivability (S), where
B(.gamma.,.delta.+1) and B(.gamma.,.delta.) are the Beta functions,
where .delta. and .gamma. are parameters of the sBG model.
S ( t | .gamma. , .delta. ) = B ( .gamma. , .delta. + t ) B (
.gamma. , .delta. ) t = 1 , 2 , Equation 2 ##EQU00002##
[0015] The example model modifier 110 modifies the baseline
retention rate model of example Equation 1 based on the sBG
distribution to create a modified retention rate model. In some
examples, the model modifier 110 substitutes Equation 2 into
Equation 1 to derive an expression for the modified retention rate
associated with the sBG model, as shown by the illustrated example
of Equation 3.
r t = .delta. + t - 1 .delta. + .gamma. + t - 1 Equation 3
##EQU00003##
[0016] The example model comparator 112 merges or combines the
baseline retention rate model (e.g., as shown in a manner
consistent with example Equation 1) with the modified retention
rate model (e.g., as shown in a manner consistent with example
Equation 3) to create a merged sBG model in a manner consistent
with example Equation 4, where .gamma. and .delta. are parameters
of the sBG model of example Equation 3.
.delta. + t - 1 .delta. + .gamma. + t - 1 = S ( t ) S ( t - 1 )
Equation 4 ##EQU00004##
[0017] Additional detail of the example model comparator 112 of
FIG. 1 is depicted in the illustrated example of FIG. 2 with
additional detail. The example model comparator 112 of FIG. 2
includes an example parameter solver 202, an example variable
definer 204, an example simplifier 206, an example linear
relationship establisher 208, an example matrix definer 210, and an
example equation generator 212. The combination of the models
results in defining a survivability variable to represent the
predicted retention rate by simplifying Equation 4 using example
Equations 5-10 below.
[0018] The example parameter solver 202 solves the merged sBG model
of example Equation 4 for a first parameter, .gamma. (gamma), as
shown in example Equation 5, where .gamma. is the first parameter
and .delta. (delta) is a second parameter of the retention rate
model.
.gamma. = ( S ( t - 1 ) - S ( t ) S ( t ) ) ( .delta. + t - 1 )
Equation 5 ##EQU00005##
[0019] For mathematical convenience, the example parameter solver
210 rearranges example Equation 5 in a manner consistent with
example Equation 6.
.gamma. ( S ( t ) S ( t - 1 ) - S ( t ) ) = .delta. + t - 1
Equation 6 ##EQU00006##
[0020] The example variable definer 204 defines a survivability
variable a.sub.t in a manner consistent with the example Equation
7. The survivability variable a.sub.t is related to the
survivability of a customer (e.g., the number of customers
surviving to time t). In some examples, the number of active
customers N(t) can be substituted for the probability that a
customer survived S(t). The base unit N(0) cancels out, making the
two expressions numerically identical.
a t = S ( t ) S ( t - 1 ) - S ( t ) Equation 7 ##EQU00007##
[0021] The example simplifier 206 substitutes the example
survivability variable a.sub.t from example Equation 7 into example
Equation 6, as shown in Equation 8.
a.sub.t.gamma.=.delta.+t-1 Equation 8:
[0022] The example linear relationship definer 208 establishes a
linear relationship between the first parameter y and a second
parameter .delta., as shown in the illustrated example of Equation
9. The example sBG model (e.g., example Equation 2) ensures that
this equality or linear relationship must be true for all values of
t. As such, the example customer retention analysis engine 100
establishes an alternate computational procedure to solve for
example parameters .gamma. and .delta.. In particular, because the
example model comparator 112 combined and/or otherwise merged the
sBG model (e.g., example Equation 2) with the baseline retention
rate model (e.g., example Equation 1), examples disclosed herein
may avoid the computationally intensive MLE procedures and modeling
iterations.
a.sub.t.gamma.-.delta.=t-1 Equation 9:
[0023] The example matrix definer 210 applies the linear
relationship (e.g., example Equation 8) to define a matrix for
multiple time periods, as shown in example Equation 10.
[ a 1 - 1 a 2 - 1 a t - 1 ] [ .gamma. .delta. ] = [ 0 1 t - 1 ]
Equation 10 ##EQU00008##
[0024] To facilitate improved calculation efficiency and/or a
reduced computational burden when calculating customer retention
rates, the example equation generator 212 generates a system of
equations based on the matrix of Equation 10. The example system of
equations is generated using the following steps and Equations
11-13. Generally speaking, the example equation generator 212
develops and/or otherwise solves the example system of equations to
derive a closed-form solution to solve for the parameters .gamma.
and .delta., which are used to calculate a retention rate without
reliance upon computationally intensive MLE procedures. In the
illustrated example, Equation 10 produces t equations (e.g., an
equation for each time period analyzed) and has two unknowns
(.gamma. and .delta.). Thus, Equation 10 creates an overdetermined
system, which may not have a solution that satisfies all of the
equations exactly. Using a linear least squares approach that
provides a closed-form solution, a value for each of the parameters
.gamma. and .delta. can be determined that best fits each of the
equations in the system.
[0025] The matrix of example Equation 10 is solved, as shown in
Equations 11- 13. Example Equation 11 is a simplified notation of
example Equation 10, where the first column in the first matrix is
a.sub.i for some number of time periods, the second column is -1,
and the matrix on the right side is i-1 for each row corresponding
to the number of time periods. Using the simplified form of example
Equation 10 in a manner consistent with example Equation 11, the
values for the parameters .gamma. and .delta. can be determined
using a set of equations that does not include any matrices (e.g.,
example Equations 19 and 20 below).
[ a i | - 1 ] [ .gamma. .delta. ] = [ 0 n - 1 ] Equation 11
##EQU00009##
[0026] Example Equation 12 produces an expression for X.sup.TX in
terms of a.sub.i and n.
X T X = [ a i - 1 ] [ a i | - 1 ] = [ a i 2 - a i - a i n ]
Equation 12 ##EQU00010##
[0027] Example Equation 13 is an expression for X.sup.Tin terms of
a.sub.i and n.
X T Y = [ a i - 1 ] [ 0 n - 1 ] = [ ( i - 1 ) a i - n ( n - 1 ) 2 ]
= [ ia i - a i - n ( n - 1 ) 2 ] Equation 13 ##EQU00011##
[0028] Example Equations 12 and 13 complete the matrix
multiplication and depict an example manner in which Equation 10
can be used to produce the expressions in terms of the known values
a.sub.i and n.
[0029] The following example Equations 14-16 represent variables
that can be defined to simplify the solution to the example matrix
(e.g., example Equation 10), where c, d, and e are the
variables.
c=.SIGMA.a.sub.i Equation 14:
d=.SIGMA.a.sub.i.sup.2 Equation 15:
e=.SIGMA.ia.sub.i Equation 16:
[0030] Example Equation 17 is the inverse of example Equation 12
with the variables c, d, and e of example Equations 14-16
substituted into the matrix.
( X T X ) - 1 = [ d - c - c n ] - 1 = 1 dn - c 2 [ n c c d ]
Equation 17 ##EQU00012##
[0031] Equation 18 is example Equation 17 multiplied by the matrix
of example Equation 13.
( X T X ) - 1 X T Y = 1 dn - c 2 [ n c c d ] [ e - c - n ( n - 1 )
2 ] Equation 18 ##EQU00013##
[0032] Example Equation 18 depicts a matrix form solution to
determine the values for parameters .gamma. and .delta.. From
example Equation 18, the parameters {circumflex over (.gamma.)} and
{circumflex over (.delta.)} are determined via matrix
multiplication using the example parameter estimator 114.
.gamma. ^ = ( n 2 ) c - 2 e + cn c 2 - dn Equation 19 .delta. ^ = 2
c ( c - e ) + d ( n - 1 ) n 2 ( c 2 - dn ) Equation 20
##EQU00014##
[0033] Using the estimated parameters {circumflex over (.gamma.)}
and {circumflex over (.delta.)} of example Equations 19 and 20, the
retention rate estimator 116 determines the retention rate using
known quantities (e.g., a time t, a number of customers still
active at time t, a ratio of customers still active at time t
compared to a baseline and/or initial number of active customers,
etc.). Customer retention is an important aspect of customer
behavior and loyalty. Modeling customer retention enables a
provider of a service or product to predict behavior and loyalty of
the customers. Predicting customer retention enables a provider of
a service or product to analyze a distribution of customer
lifetimes. Customer retention data can be used by businesses to
improve marketing to customers and/or customer loyalty
programs.
[0034] The system of linear equations defined by Equations 19 and
20 can easily be solved with less computational power than needed
to determine the retention rate using conventional maximum
likelihood procedures. The parameters {circumflex over (.gamma.)}
and {circumflex over (.delta.)} are substituted into Equation 3 to
solve for the retention rate. After the initial derivation of
Equations 19 and 20, the closed form solution needs only to use
Equations 19 and 20 to solve for the parameters that can be
substituted into Equation 3 to determine the retention rate. Thus,
instead of the typical iterative process used by the current MLE
procedures, the closed form solution is a relatively simple and
less computationally burdensome process to determine the retention
rate, which does not require exhaustive iteration and uses less
computing power of a processor.
[0035] While example manners of implementing the analysis engine
100 of FIG. 1 and the model comparator 112 of FIG. 2. are
illustrated in FIGS. 3 and 4, one or more of the elements,
processes and/or devices illustrated in FIGS. 3 and 4 may be
combined, divided, re-arranged, omitted, eliminated and/or
implemented in any other way. Further, the example survivability
data retriever 104, the example retention rate model generator 106,
the example sBG distribution generator 108, the example model
modifier 110, the example model comparator 112, the example
parameter estimator 114, the example retention rate estimator 116,
the example parameter solver 202, the example variable definer 204,
the example simplifier 206, the example linear relationship
establisher 208, the example matrix definer 210, the example
equation generator 212, and/or, more generally, the example
customer retention analysis engine 100 of FIGS. 1 and 2 may be
implemented by hardware, software, firmware and/or any combination
of hardware, software and/or firmware. Thus, for example, any of
the example survivability data retriever 104, the example retention
rate model generator 106, the example sBG distribution generator
108, the example model modifier 110, the example model comparator
112, the example parameter estimator 114, the example retention
rate estimator 116, the example parameter solver 202, the example
variable definer 204, the example simplifier 206, the example
linear relationship establisher 208, the example matrix definer
210, the example equation generator 212, and/or, more generally,
the example customer retention analysis engine 100 could be
implemented by one or more analog or digital circuit(s), logic
circuits, programmable processor(s), application specific
integrated circuit(s) (ASIC(s)), programmable logic device(s)
(PLD(s)) and/or field programmable logic device(s) (FPLD(s)). When
reading any of the apparatus or system claims of this patent to
cover a purely software and/or firmware implementation, at least
one of the example, the example survivability data retriever 104,
the example retention rate model generator 106, the example sBG
distribution generator 108, the example model modifier 110, the
example model comparator 112, the example parameter estimator 114,
the example retention rate estimator 116, the example parameter
solver 202, the example variable definer 204, the example
simplifier 206, the example linear relationship establisher 208,
the example matrix definer 210, the example equation generator 212,
and/or, more generally, the example customer retention analysis
engine 100 is/are hereby expressly defined to include a tangible
computer readable storage device or storage disk such as a memory,
a digital versatile disk (DVD), a compact disk (CD), a Blu-ray
disk, etc. storing the software and/or firmware. Further still, the
example customer retention analysis engine 100 of FIG. 1 may
include one or more elements, processes and/or devices in addition
to, or instead of, those illustrated in FIGS. 1 and 2, and/or may
include more than one of any or all of the illustrated elements,
processes and devices.
[0036] Flowcharts representative of example machine readable
instructions for implementing the example customer retention
analysis engine 100 of FIG. 1 are shown in FIGS. 3 and 4. In these
examples, the machine readable instructions comprise a program for
execution by a processor such as the processor 512 shown in the
example processor platform 500 discussed below in connection with
FIG. 5. The programs may be embodied in software stored on a
tangible computer readable storage medium such as a CD-ROM, a
floppy disk, a hard drive, a digital versatile disk (DVD), a
Blu-ray disk, or a memory associated with the processor 512, but
the entire program and/or parts thereof could alternatively be
executed by a device other than the processor 512 and/or embodied
in firmware or dedicated hardware. Further, although the example
programs are described with reference to the flowcharts illustrated
in FIGS. 3 and 4, many other methods of implementing the example
customer retention analysis engine 100 may alternatively be used.
For example, the order of execution of the blocks may be changed,
and/or some of the blocks described may be changed, eliminated, or
combined.
[0037] As mentioned above, the example processes of FIGS. 3 and 4
may be implemented using coded instructions (e.g., computer and/or
machine readable instructions) stored on a tangible computer
readable storage medium such as a hard disk drive, a flash memory,
a read-only memory (ROM), a compact disk (CD), a digital versatile
disk (DVD), a cache, a random-access memory (RAM) and/or any other
storage device or storage disk in which information is stored for
any duration (e.g., for extended time periods, permanently, for
brief instances, for temporarily buffering, and/or for caching of
the information). As used herein, the term tangible computer
readable storage medium is expressly defined to include any type of
computer readable storage device and/or storage disk and to exclude
propagating signals and transmission media. As used herein,
"tangible computer readable storage medium" and "tangible machine
readable storage medium" are used interchangeably. Additionally or
alternatively, the example processes of FIGS. 3 and 4 may be
implemented using coded instructions (e.g., computer and/or machine
readable instructions) stored on a non-transitory computer and/or
machine readable medium such as a hard disk drive, a flash memory,
a read-only memory, a compact disk, a digital versatile disk, a
cache, a random-access memory and/or any other storage device or
storage disk in which information is stored for any duration (e.g.,
for extended time periods, permanently, for brief instances, for
temporarily buffering, and/or for caching of the information). As
used herein, the term non-transitory computer readable medium is
expressly defined to include any type of computer readable storage
device and/or storage disk and to exclude propagating signals and
transmission media. As used herein, when the phrase "at least" is
used as the transition term in a preamble of a claim, it is
open-ended in the same manner as the term "comprising" is open
ended.
[0038] FIG. 3 is a flowchart 300 representative of example machine
readable instructions that may be executed to implement the example
customer retention analysis engine 100 of FIG. 1. The instructions
begin by instructing the survivability data retriever 104 to
retrieve customer survivability data for a first observed duration
of interest from the example customer data storage 102 (block 302).
The example retention rate model generator 106 generates a baseline
retention rate model based on survivability data associated with an
observed duration of interest (block 304). In some examples, the
baseline retention rate model may be generated in a manner
consistent with example Equation 1. The example sBG distribution
generator 108 generates a shifted-beta-geometric (sBG) model based
on the survivability data (block 306). In some examples, the sBG
distribution is generated in a manner consistent with example
Equation 2. The example model modifier 110 modifies the baseline
retention rate model based on the sBG distribution to generate a
modified retention rate model (block 308). As described above, the
modified retention rate model may be generated in a manner
consistent with example Equation 3.
[0039] A model comparator 112 merges the modified retention rate
model (e.g., example Equation 3) with the baseline retention rate
model (e.g., example Equation 1) to generate a merged sBG model
(block 310). The merged sBG model includes sBG model parameters
(e.g., .gamma., .delta.) operative to determine the retention rate.
The merged sBG model may be generated in a manner consistent with
Equation 4. Generating the merged sBG model reduces a computational
burden typically required to calculate customer retention using the
MLE procedures. As described in further detail below, the example
flowchart 310 of FIG. 4 represents example instructions that may be
implemented to generate a system of equations to determine values
for the sBG parameters (e.g., .gamma. and .delta.) of the merged
sBG model.
[0040] The example parameter estimator 114 determines the sBG
parameter values of the model the system of equations derived using
the example model comparator 112 and the instructions depicted as
flowchart 310 (block 312). For example, Equations 19 and 20 may be
used to estimate the sBG parameters. The example retention rate
estimator 116 determines the retention rate based on the sBG
parameters, other known quantities, and the merged sBG model (block
314). The retention rate may be determined in a manner consistent
with Equation 3. After determining the retention rate (block 314),
the illustrated example of FIG. 3 is complete. Equations 19 and 20
represent a closed form solution which can be used to predict the
retention rate. Thus, instead of the typical iterative process used
by the current Maximum Likelihood procedures, the closed form
solution is a relatively simple and less computationally burdensome
process to determine the retention rate, which does not require
exhaustive iteration and uses less computing power of a
processor.
[0041] FIG. 4 illustrates additional details of the flowchart 300
described above in connection with FIG. 3 to compare the modified
retention rate model. The instructions begin by the example
parameter solver 202 solving the sBG model for a first sBG
parameter (e.g., .gamma.) (block 402). Solving for the first
parameter may be completed in a manner consistent with example
Equation 5. For mathematical convenience, example Equation 5 may
also be written in a manner consistent with example Equation 6. The
example variable definer 204 defines a survivability variable
(e.g., a.sub.t) related to customer survivability and based on the
merged sBG model (block 404). The example survivability variable
may be depicted in a manner consistent with at and/or implemented
in a manner consistent with example Equation 7. The example
simplifier 206 simplifies the sBG model depicted in example
Equation 4 by substituting the example survivability variable
(block 406). The sBG model may be simplified in a manner consistent
with example Equation 8.
[0042] The example linear relationship determiner 208 defines a
linear relationship between the first sBG parameter (e.g., .gamma.)
and the second sBG parameter (e.g., .delta.) (block 408). The
linear relationship is defined in a manner consistent with example
Equation 9. The example matrix definer 210 defines a matrix
equation for multiple time periods based on the linear relationship
between the example sBG parameters (block 410). The matrix may be
defined in a manner consistent with example Equation 10. The
example equation generator 212 generates a system of equations to
be implemented by the example parameter estimator 114 to determine
the customer retention rate by solving the matrix (block 412). For
example, the matrix may be solved in a manner consistent with using
Equations 11-18. The system of equations may be defined for the sBG
parameters in a manner consistent with Equations 19 and 20. The
system of equations defined by the equation generator 212 may be
used by the parameter estimator 114 in a manner consistent with the
instructions depicted by the flowchart 300 of FIG. 3.
[0043] FIG. 5 is a block diagram of an example processor platform
500 capable of executing the instructions of FIGS. 3 and 4 to
implement the apparatus of FIGS. 1 and 2. The processor platform
500 can be, for example, a server, a personal computer, a mobile
device (e.g., a cell phone, a smart phone, a tablet such as an
iPad), a personal digital assistant (PDA), an Internet appliance, a
gaming console, a set top box, or any other type of computing
device.
[0044] The processor platform 500 of the illustrated example
includes a processor 512. The processor 512 of the illustrated
example is hardware. For example, the processor 512 can be
implemented by one or more integrated circuits, logic circuits,
microprocessors or controllers from any desired family or
manufacturer.
[0045] The processor 512 of the illustrated example includes a
local memory 513 (e.g., a cache). The processor 512 of the
illustrated example is in communication with a main memory
including a volatile memory 514 and a non-volatile memory 516 via a
bus 518. The volatile memory 514 may be implemented by Synchronous
Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory
(DRAM), RAMBUS Dynamic Random Access Memory (RDRAM) and/or any
other type of random access memory device. The non-volatile memory
516 may be implemented by flash memory and/or any other desired
type of memory device. Access to the main memory 514, 516 is
controlled by a memory controller.
[0046] The processor platform 500 of the illustrated example also
includes an interface circuit 520. The interface circuit 520 may be
implemented by any type of interface standard, such as an Ethernet
interface, a universal serial bus (USB), and/or a PCI express
interface.
[0047] In the illustrated example, one or more input devices 522
are connected to the interface circuit 520. The input device(s) 522
permit(s) a user to enter data and commands into the processor
1012. The input device(s) can be implemented by, for example, an
audio sensor, a microphone, a camera (still or video), a keyboard,
a button, a mouse, a touchscreen, a track-pad, a trackball,
isopoint and/or a voice recognition system.
[0048] One or more output devices 524 are also connected to the
interface circuit 520 of the illustrated example. The output
devices 1024 can be implemented, for example, by display devices
(e.g., a light emitting diode (LED), an organic light emitting
diode (OLED), a liquid crystal display, a cathode ray tube display
(CRT), a touchscreen, a tactile output device, a light emitting
diode (LED), a printer and/or speakers). The interface circuit 520
of the illustrated example, thus, typically includes a graphics
driver card, a graphics driver chip or a graphics driver
processor.
[0049] The interface circuit 520 of the illustrated example also
includes a communication device such as a transmitter, a receiver,
a transceiver, a modem and/or network interface card to facilitate
exchange of data with external machines (e.g., computing devices of
any kind) via a network 526 (e.g., an Ethernet connection, a
digital subscriber line (DSL), a telephone line, coaxial cable, a
cellular telephone system, etc.).
[0050] The processor platform 500 of the illustrated example also
includes one or more mass storage devices 528 for storing software
and/or data. Examples of such mass storage devices 528 include
floppy disk drives, hard drive disks, compact disk drives, Blu-ray
disk drives, RAID systems, and digital versatile disk (DVD)
drives.
[0051] The coded instructions 532 of FIGS. 3 and 4 may be stored in
the mass storage device 528, in the volatile memory 514, in the
non-volatile memory 516, and/or on a removable tangible computer
readable storage medium such as a CD or DVD.
[0052] From the foregoing, it will be appreciated that the above
disclosed methods, apparatus and articles of manufacture disclose
determining a retention rate of customers using a closed form
solution that reduces the amount of computing power and/or
resources used by the processor relative to current methods of
determining a retention rate of customers, such as an iterative
maximum likelihood procedure.
[0053] Although certain example methods, apparatus and articles of
manufacture have been disclosed herein, the scope of coverage of
this patent is not limited thereto. On the contrary, this patent
covers all methods, apparatus and articles of manufacture fairly
falling within the scope of the claims of this patent.
* * * * *